can you tell me what 's the acceptable sample size for
PLS estimation since

it declares the small to medium sample size required
comparing others such

as LISREL and AMOS?

thx

Answer:

When you go through the formal model specification and the basic
PLS estimation process, the

requirements for
sample size becomes reasonably clear for all three stages of the estimation
process. It has to do with the fact that either simple or multiple
regressions is performed depending on the modefor
each block of indicators and the inner weighting scheme. Due to the partial
nature of theestimation procedure where
only a portion of the model is involved at any one time, only the part that
requires the largest multiple regression becomes important. And while stage 2
and 3 are equivalent insample size
requirements, stage 1 may not require as large a sample size contingent on whichinner approximation is selected.

Overall, for adequate power at stages 2 and 3, you simply have
to look at the model specification

or
equivalently the graphical model such as that depicted in Figure 1 and find the
largest of twopossibilities: 1) the block
with the largest number of formative indicators (i.e., largestmeasurement
equation) or 2) the dependent LV with the largest number of independent LVsimpacting it (i.e., largest structural equation).
If you use a regression heuristic of tencases
per predictor, the sample size requirement would be ten times either 1) or 2),
whichever isthe greater. For a more
accurate assessment, you would specify the effect size for each regressionanalysis and look up the power tables provided by
Cohen (1988) or Greenís (1991)approximation
to these tables.

Using Figure 1 as an example, the only block with formative
indicators consists of four indicators impacting
x2. The dependent
LV with the largest number of independent LVs impacting it is h2with three paths going into it. Thus, the largest
regression at any one time consists of fourindependent
variables. Assuming a medium effect size as defined by Cohen (1988), you wouldneed a minimum sample size of 84 to obtain a power
of 0.80. With a large effect size, the samplerequirement
drops to 39.

For stage 1, the use of a path weighting scheme would result in
the same sample requirements as necessary
for stages 2 and 3. But with the use of a factor or centroid weighting scheme,
onlysimple regressions between the LVs are
performed in calculating the weights to be used for theinside
approximation. In this situation, only the measurement model with formative
indicatorsbecomes the critical factor in
sample size requirements. Had all latent variables been modeled asreflective
(mode A), the use of either a factor or centroid weighting scheme would entail
only aseries of simple regressions during
the entire stage 1 process resulting in a minimum sample sizerequirement
of 53 and 24 for medium and large effect sizes.

In fact, the minimum sample size required to assess component
loadings for reflective indicators is likely
even smaller. Given that the standard requirement for loadings are normally set
at 0.60 orabove, the effect size of
component loadings are larger than what is considered large in regressionpower analysis (i.e., f
2of 0.35, Cohen, 1988). For
example, a 0.60 loading represents an f2effect size
of 0.56 and requires a sample size of 15 to obtain a power of 0.80 for
detection. Thissituation is demonstrated
partly in a Monte Carlo study where sample sizes of 20 could notdetect
structural paths of 0.40, but easily detected loadings of 0.60 and 0.80.

More information about PLS and
sample size can be obtained from the following paper: